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Credible Persuasion

We propose a new notion of credibility for Bayesian persuasion problems. A disclosure policy is credible if the sender cannot profit from tampering with her messages while keeping the message distribution unchanged. We show that the credibility of a disclosure policy is equivalent to a cyclical monotonicity condition on its induced distribution over states and actions. We also characterize how credibility restricts the Sender's ability to persuade under different payoff structures. In particular, when the sender's payoff is state-independent, all disclosure policies are credible. We apply our results to the market for lemons, and show that no useful information can be credibly disclosed by the seller, even though a seller who can commit to her disclosure policy would perfectly reveal her private information to maximize profit.